Problem: $f(x) = -3x^{2}-1$ What is the range of $f(x)$ ?
Explanation: Consider the range of $-3x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $-3$ flips the range to $\{\, y \mid y \le 0 \,\}$ To get $-3x^{2}-1$, we subtract $1$. So the range becomes: $\{\, y \mid y ≤ -1 \,\}$.